Abstract
A nonlinear mechanical system with time delay shows noise and chatter vibration. When the time delay is large, the system may be damaged. Therefore, it is important to analyze the nonlinear system with time delay. However, the nonlinear system with time delay is described by a difference -differential equation which is difficult to solve. This paper discusses the forced vibration of the system. In order to analyze the system, we used an averaging method for a functional differential equation. This method can derive the stability condition of the forced vibration of the system. We show that the averaging method yields a proper solution. Not only when the system has small time delay but also when it has large time delay, the solution approximates the behavior of the system adequately.
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